magnetic properties of solids the magnetic property of a solid originates from collective behavior of its atom’s magnetic dipole moment. The magnetic moment of an atom, arises due to three effects. (i) The orbital motion of the electrons, (ii) the spin of the electrons, and (iii) the spin of the nucleons inside the nucleus. Out of these the magnetic moment due to the nucleus is comparatively very small, and its effect can be ignored.
The rotational magnetic dipole moment of the electron, called the orbital magnetic moment, can be obtained purely from classical considerations. This is given as,
m
= (e m)/(2 me)where m is the magnetic quantum number* . For a given value of l, m can take 2l+1 integer values, from -l to +l. Now consider l=1, for which m can take three values -1, 0, +1. This physically means the component of angular momentum along an external magnetic field direction can take three values. -h, 0, h. It can be shown classically that the corresponding values of orbital magnetic moment are,
-(eh/2me), 0, and (eh/2me).
Obviously in a filled shell the orbital magnetic moments cancel giving no contribution. It is only the outer unfilled shells that contribute to the orbital magnetic moment. If however the unfilled shell lies in the periphery of the atom, as in the case of iron group (Sc, Ti, V, Cr, Mn, Co, Ni), they are highly susceptible to interactions with neighboring atoms in the lattice. As a result their orbital magnetic moment cannot orient with the external magnetic field. In rare earth element ( atomic no. 58-71),where unfilled shells are relatively deep inside the atom, the orbital dipole moment contributes towards the magnetization, M.
An atom may have all filled shells, but in the presence of an external magnetic field, the atomic dipole moments do not cancel each other. A pair of electrons with magnetic quantum number +l and -l, rotate in the opposite sense. In the presence of an external magnetic field, as a consequence of Lenz’s law, magnetic moment of one of the electrons will be lowered and for the other it will be raised. This will result in unbalanced orbital magnetic moment. This gives rise to diamagnetism, an effect in which a material repels an external magnetic field. The force is weak, and in atoms which also posses spin magnetic moment, the effect is completely suppressed.
Next we consider the effect of the spin of the electron which is the most significant as regards to the magnetic properties of the iron group. The possible values of spin quantum number, m are =1/2 and -1/2. This physically means the spin of the electron has only possible orientations with the external magnetic field either parallel or anti parallel with spin values +(1/2)h and -(1/2)h. The corresponding values of magnetic dipole moments are eh/2me and -eh/2me , a result obtained from quantum theory.
Again completely filled shells will not produce any resultant spin magnetic moment as the spins of electron pairs are oppositely oriented. Only the outer unpaired electron gives rise to spin dipole moment, as in the case of paramagnetic solids. The thermal motion makes the magnetic moments of the atoms randomly oriented, giving zero net magnetization at normal room temperatures. When the temperature is lowered or the material is kept in external magnetic field the magnetic moments will align giving rise to magnetization. It has been observed that for the paramagnetic materials, susceptibility, c varies inversely with temperature (Curie’s law*).
In the first transition series all the elements from scandium to nickel have unpaired electrons (see Table aIII) giving rise to large spin dipole moment. But for the elements scandium, titanium, vanadium, chromium, and manganese radius of 3d orbitals in the atom is large resulting in the overlap of orbitals in the solid state. In the resulting 3d band the electrons pair up with opposite orientation canceling their spin magnetic moment. These are known as antiferromagnetic materials.
In ferromagnetic materials (iron, cobalt, and nickel) 3d orbital radius is comparatively small and the electrons in the neighboring atoms align themselves thereby lowering the spin dependent electrostatic energy. In the solid the 4s energy band overlaps with the 3d band. The 4s unpaired electron remains most of the time oppositely oriented to the 3d electrons. This results in the lowering of magnetic moment of the atom. Thus in iron there are 4 unpaired electrons in the 3d orbital, but in the solid it has 2.2 Bohr magneton as its magnetic moment per atom. The magnetic moment per atom in cobalt is 1.7 and that for nickel 0.6 Bohr magneton.
Each ferromagnetic material has a characteristic temperature, called the Curie temperature, Q beyond which the material behaves like a paramagnetic material. The value of Q for iron, cobalt and nickel are 1093K, 1393K and 693K respectively.
Ferromagnetic domains: The atoms of an unmagnetized sample of ferromagnetic material group into domain structure i.e. regions of size 10-6 m where the magnetic dipoles are parallel. The direction of orientation varies in such a way so as to make the resultant magnetization zero. It is because of these domains a sample of ferromagnetic material in the presence of external magnetic field H shows hysteresis. Fig, m8 shows a typical hysteresis loop, for a ferromagnetic solid. When the sample is subjected to external magnetic field, the domains align themselves with external field direction. Also the domains which are in the direction of external field grow bigger. Ultimately the whole material becomes a single domain. At this point saturation is reached. Now when the reverse process is done, the curve is not retraced.
Ferrimagnetism: It results from antiferrimagnetic interaction between two ions which have unequal magnetic moment resulting in net magnetism. Consider magnetite (FeO.Fe2O3) which contains two types of iron ions, Fe++ and Fe+++ and four O- - ions. The oxygen ions are arranged in closed packed fcc* structure. There are two types of voids in this structure; tetrahedral voids surrounded by four O- - ions and octahedral voids surrounded by eight O- - ions. Octahedral voids are twice the number of tetrahedral voids. The Fe++ and Fe+++ ions are small in size. These ions occupy the voids of the oxygen ions. Fe+++ ions occupy all the tetrahedral and half the octahedral sites. The other half of octahedral sites are occupied by Fe++ ions. There is anti ferromagnetic coupling between ions in the octahedral and tetrahedral sites. This results in cancellation of magnetic moments of Fe+++ ions, and magnetization of magnetite is equal to that produced by Fe++ ions alone, i.e. 4 Bohr magneton per molecule.
Ferrimagnetic materials called ferrites have high resistivity. Consequently the eddy current loss is small in ferrites. Transformer cores for high frequency are made of ferrites.